System and method of representing a line segment with two thin triangles

A method to graphically represent a line segment by two triangles, the method comprising:

• receiving at a graphics processor a first vertex and a second vertex of a line segment;
• determining by the graphics processor a scaling factor that is equal to 4 to a power of an integer L;
• inputting an input value to a lookup table by the graphics processor, the input value comprising 2 to a negative power of L times a dot product of a normal vector to the line segment with itself;
• receiving by the graphics processor from the lookup table an output value that equals a reciprocal square root of the input to the lookup table;
• determining by the graphics processor a unit normal vector to the line segment by dividing the normal vector to the line segment by the output value received from the lookup table;
• determining by the graphics processor a first half normal vector and a second half normal vectors to the line segment from the unit normal vector and the first vertex and the second vertex of the line segment;
• determining by the graphics processor a first triangle and a second triangle based on the first and second half normal vectors and the first vertex and the second vertex of the line segment, the first and second triangles each comprising a hypotenuse and being joined together by their hypotenuses;
• and
• graphically rendering the line segment by the graphics processor by rendering the first and second triangles.

A method to graphically represent a line segment by two triangles, the method comprising:

• receiving at a graphics processor a first vertex v0 and a second vertex v1 of a line segment;
• determining by the graphics processor a scaling factor P=4L in which L is an integer value given by L=└log4(n·n)┘ in which n is a normal vector to the line segment, and n·n is a dot product of the normal vector n with itself;
• inputting an input value a into a lookup table by the graphics processor, the input value comprising a=2−2L (n·n);
• receiving by the graphics processor from the lookup table an output value b=S(2−2L(n·n));
• determining by the graphics processor a unit normal vector {circumflex over (n)} to the line segment by multiplying the normal vector n to the line segment by the output value b received from the lookup table;
• determining by the graphics processor a first normal half vector h and a second half normal vector h to the line segment from the unit normal vector {circumflex over (n)} and the first vertex v0 and the second vertex v1 of the line segment;
• determining by the graphics processor a first triangle and a second triangle based on the first half normal vector h and the second half normal vector h and the first vertex v0 and the second vertex v1 of the line segment, the first and second triangles each comprising a hypotenuse and being joined together by their hypotenuses;
• and
• graphically rendering the line segment by the graphics processor by rendering the first and second triangles.